DifferentialSolver

DifferentialSolver#

The DifferentialSolver is a differential inverse kinematics (IK) controller designed for robot manipulators. It computes joint-space commands to achieve desired end-effector positions or poses using various Jacobian-based methods.

Key Features#

  • Supports multiple IK methods: pseudo-inverse (pinv), singular value decomposition (svd), transpose (trans), and damped least squares (dls)

  • Configurable for position or pose control, with absolute or relative modes

  • Efficient batch computation for multiple environments

  • Flexible configuration via DifferentialSolverCfg

Configuration Example#

from embodichain.data import get_data_path
from embodichain.lab.sim.solvers.differential_solver import DifferentialSolver
from embodichain.lab.sim.solvers.differential_solver import DifferentialSolverCfg

cfg = DifferentialSolverCfg(
    urdf_path=get_data_path("UniversalRobots/UR5/UR5.urdf"),
    joint_names=["joint1", "joint2", "joint3", "joint4", "joint5", "joint6"],
    end_link_name="ee_link",
    root_link_name="base_link",
    command_type="pose",
    use_relative_mode=False,
    ik_method="pinv",
    ik_params={"k_val": 1.0}
)

solver = DifferentialSolver(cfg)

Main Methods#

  • get_fk(self, qpos: torch.Tensor) -> torch.Tensor
    Computes the end-effector pose (homogeneous transformation matrix) for the given joint positions.

    Parameters:

    • qpos (torch.Tensor or list[float]): Joint positions, shape (num_envs, num_joints) or (num_joints,).

    Returns:

    • torch.Tensor: End-effector pose(s), shape (num_envs, 4, 4).

    Example:

  fk = solver.get_fk(qpos=[0.0, 0.0, 0.0, 1.5708, 0.0, 0.0])
  print(fk)
  # Output:
  # tensor([[[ 0.0,     -1.0,      0.0,     -0.722600],
  #          [ 0.0,      0.0,     -1.0,     -0.191450],
  #          [ 1.0,      0.0,      0.0,      0.079159],
  #          [ 0.0,      0.0,      0.0,      1.0     ]]])

  • get_ik(self, target_xpos: torch.Tensor, qpos_seed: torch.Tensor = None, return_all_solutions: bool = False, jacobian: torch.Tensor = None) -> Tuple[torch.Tensor, torch.Tensor]
    Computes joint positions (inverse kinematics) for the given target end-effector pose.

    Parameters:

    • target_xpos (torch.Tensor): Target end-effector pose(s), shape (num_envs, 4, 4).

    • qpos_seed (torch.Tensor, optional): Initial guess for joint positions, shape (num_envs, num_joints). If None, a default is used.

    • return_all_solutions (bool, optional): If True, returns all possible solutions. Default is False.

    • jacobian (torch.Tensor, optional): Custom Jacobian. Usually not required.

    Returns:

    • Tuple[torch.Tensor, torch.Tensor]:

      • First element: Joint positions, shape (num_envs, num_joints).

      • Second element: Convergence info or error for each environment.

    Example:

  import torch
  xpos = torch.tensor([[[ 0.0,     -1.0,      0.0,     -0.722600],
                        [ 0.0,      0.0,     -1.0,     -0.191450],
                        [ 1.0,      0.0,      0.0,      0.079159],
                        [ 0.0,      0.0,      0.0,      1.0     ]]])
  qpos_seed = torch.zeros((1, 6))
  qpos_sol, info = solver.get_ik(target_xpos=xpos)
  print("IK solution:", qpos_sol)
  print("Convergence info:", info)
  # IK solution: tensor([True])
  # Convergence info: tensor([[0.0, -0.231429, 0.353367, 0.893100, 0.0, 0.555758]])

Tip:

  • get_fk is for forward kinematics (joint to end-effector), get_ik is for inverse kinematics (end-effector to joint).

  • For batch computation, the first dimension of qpos and target_xpos is the batch size.

IK Methods Supported#

  • pinv: Jacobian pseudo-inverse

  • svd: Singular value decomposition

  • trans: Jacobian transpose

  • dls: Damped least squares

References#

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